Big Idea:
Students will write formal proofs showing how triangles are congruent when two corresponding angles and the included side are congruent.

In a previous lesson, students investigated the side-angle-side postulate where they identified the included angle between two sides in order to prove two triangles congruent. Students should have fluency with identifying and labeling parts of a triangle. This do now checks students’ ability to correctly identify the included angle between two sides in a triangle. They are given a complex diagram and asked to identify the included angle between two specific sides (MP1). It leads into the Mini-Lesson where students will identify the included side between two angles in a triangle.

Resources (2)

Resources

As in the Do Now, to begin the mini-lesson students are given a complex triangle and asked to identify parts of the triangle. Students look at two angles and identify the sides included between the two angles. This activity leads to a review of the Angle-Side-Angle Postulate, which students first looked at in a previous lesson. Students can refer back to the charts they completed in that lesson for a definition of the ASA postulate.

Resources (2)

Resources

In this Activity, students are given six diagrams with given statements. For the first three questions, students write formal two-column proofs. In the last three questions, students can write two-column or paragraph proofs.

For the first few minutes of the activity, I have the students look at the problems and brainstorm what they need to do in order to prove the statements. After they have a plan, I ask them to begin writing their formal proofs. As they work, I circulate around the room and help them with the flow and precision of their proofs, as needed.

After about 20 minutes I plan to choose several students to present their proofs of questions four through six on the document camera. I call on students who did their proofs using different methods to compare their results.

Resources (2)

Resources

For today's Exit Ticket I present students with one of the diagrams from the earlier activity and I ask them to identify and label corresponding congruent parts of the triangles. Since they have already proved that the parts were congruent in the activity, the task should go smoothly. This task prepares students for the tomorrow's lesson on writing proofs involving corresponding parts of congruent triangles.